I am interested in the analysis of partial differential equations and the conception of structure preserving schemes for their numerical resolution.
Keywords: partial differential equations (PDEs), numerical analysis, kinetic PDEs, parabolic PDEs, asymptotic behaviors, entropy methods, hypocoercivity, macroscopic limits, non-conforming schemes, positive polynomials, semiconductors, particle accelerator physics, plasma physics, life sciences.
Discrete Sobolev and Trudinger inequalities on polyhedral meshes - (preprint)
with Ariane Trescases and Antoine Zurek - submitted, 2026.
Fractional hypocoercivity in bounded domains in the anomalous diffusion limit - (preprint)
with Marc Pegon and Isabelle Tristani - 2025.
Existence of solutions and uniform bounds for the stationary semiconductor equations with generation and ionic carriers - (preprint)
with Dilara Abdel, Alain Blaustein, Claire Chainais-Hillairet, and Julien Moatti - submitted, 2025.
Well-posedness and long-time behavior for self-consistent Vlasov-Fokker-Planck equations with general potentials - (preprint)
with Pierre Gervais - submitted, 2024.
Convergence and long-time behavior of finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion - (preprint)
with Clément Cancès and Annamaria Massimini - IMA Journal of Numerical Analysis, 2026.
Infinitely many saturated travelling waves for a degenerate Fisher-KPP equation not in divergence form - (preprint)
with Matthieu Alfaro and Andrea Natale - Journal of Differential Equations, 2026.
A finite volume scheme for the local sensing chemotaxis model - (preprint)
with Ariane Trescases and Antoine Zurek - SMAI Journal of Computational Mathematics, 2025.
Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models - (preprint)
with Dilara Abdel, Martin Ziegler, Claire Chainais-Hillairet, Benjamin Spetzler and Patricio Farrell - Computers & Mathematics with Applications, 2025.
Charge transport systems with Fermi-Dirac statistics for memristors - (preprint)
with Ansgar Jüngel and Stefan Portisch - Journal of Nonlinear Science, 2025.
Wasserstein contraction for the stochastic Morris-Lecar neuron model - (preprint)
with Pierre Monmarché and Benoît Perthame - Kinetic and Related Models, 2025.
On a Vlasov-Fokker-Planck equation for stored electron beams - (preprint)
with Ludovic Cesbron - Journal of Differential Equations, 2024.
Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells - (preprint)
with Dilara Abdel, Claire Chainais-Hillairet and Patricio Farrell - IMA Journal of Numerical Analysis, 2024.
Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system - (preprint)
with Antoine Zurek - ESAIM: Mathematical Modelling and Numerical Analysis, 2023.
On a structure-preserving numerical method for fractional Fokker-Planck equations - (preprint)
with Nathalie Ayi, Hélène Hivert and Isabelle Tristani - Mathematics of Computation, 2023.
Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches - (preprint)
with Claire Chainais-Hillairet, Simon Lemaire and Julien Moatti - Numerische Mathematik, 2022.
A Fokker-Planck approach to the study of robustness in gene expression - (preprint)
with Pierre Degond and Sepideh Mirrahimi - Mathematical Biosciences and Engineering, 2020.
Large time behavior of nonlinear finite volume schemes for convection-diffusion equations - (preprint)
with Clément Cancès, Claire Chainais-Hillairet and Stella Krell - SIAM Journal on Numerical Analysis, 2020.
A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium - (full text)
with Nathalie Ayi, Hélène Hivert and Isabelle Tristani - Comptes Rendus, Mathématique, 2020.
Computation of sum of squares polynomials from data points - (preprint)
with Bruno Després - SIAM Journal on Numerical Analysis, 2020.
A projection algorithm on the set of polynomials with two bounds - (preprint)
with Martin Campos Pinto, Frédérique Charles and Bruno Després - Numerical Algorithms, 2020.
Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations - (preprint)
with Marianne Bessemoulin-Chatard and Thomas Rey - Mathematics of Computation, 2019.
Large-time behavior of a family of finite volume schemes for boundary-driven convection-diffusion equations - (preprint)
with Claire Chainais-Hillairet - IMA Journal of Numerical Analysis, 2019.
Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations - (preprint)
with L. Miguel Rodrigues - Kinetic and Related Models, 2019.
Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit - (preprint)
with L. Miguel Rodrigues - Journal of Statistical Physics, 2018.
A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure - (preprint)
with Francis Filbet - Numerische Mathematik, 2017.
On massless electron limit for a multispecies kinetic system with external magnetic field - (preprint)
Journal of Differential Equations, 2016.
Synchronization of Synchrotron Radiation Bursts during a spatio-temporal Instability in accelerator-Based source - (preprint)
with Clément Évain, Abdoul-Aziz Diallo, Éléonore Roussel, Christophe Szwaj, Marie-Agnès Tordeux, Fernand Ribeiro, Marie Labat, Nicolas Hubert, Jean-Blaise Brubach, Pascale Roy, Serge Bielawski - submitted, 2026.
Finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion - (preprint)
with Clément Cancès and Annamaria Massimini - Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems. FVCA 2023.
L∞ bounds for numerical solutions of noncoercive convection-diffusion equations - (preprint)
with Claire Chainais-Hillairet - Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 2020.
Correction to: Polynomials with bounds and numerical analysis - (Erratum - Original paper here)
with Bruno Després - Numerical Algorithms, 2017.
Modelling and simulating a multispecies plasma - (Full text)
with Mehdi Badsi - ESAIM Proceedings, 2016.
Asymptotic and numerical analysis of kinetic and fluid models for the transport of charged particles - (Full text)
PhD Thesis, Université Lyon 1, 2017